2018 Chapter Competition Sprint Round Problems 1 30

Transcription

1 Chapter Competition Sprint Round Problems 1 30 HONOR PLEDGE I pledge to uphold the highest principles of honesty and integrity as a Mathlete. I will neither give nor accept unauthorized assistance of any kind. I will not copy another s work and submit it as my own. I understand that any competitor found to be in violation of this honor pledge is subject to disqualification. Signature Date Printed Name School DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO. This section of the competition consists of 30 problems. You will have 40 minutes to complete all the problems. You are not allowed to use calculators, books or other aids during this round. If you are wearing a calculator wrist watch, please give it to your proctor now. Calculations may be done on scratch paper. All answers must be complete, legible and simplified to lowest terms. Record only final answers in the blanks in the left-hand column of the competition booklet. If you complete the problems before time is called, use the remaining time to check your answers. In each written round of the competition, the required unit for the answer is included in the answer blank. The plural form of the unit is always used, even if the answer appears to require the singular form of the unit. The unit provided in the answer blank is the only form of the answer that will be accepted. Total Correct Scorer s Initials 2018 MATHCOUNTS National Competition Sponsor National Sponsors Raytheon Company Northrop Grumman Foundation U.S. Department of Defense National Society of Professional Engineers CNA Insurance Phillips 66 Texas Instruments Incorporated 3Mgives Art of Problem Solving NextThought Founding Sponsors: National Society of Professional Engineers, National Council of Teachers of Mathematics and CNA Foundation Copyright MATHCOUNTS, Inc All rights reserved. 02-C18SPR

2 1. What integer is closest in value to ? 2. minutes How many minutes past 2 o clock is the time displayed on the clock shown here? 3. $ Rufus has $835 in his checking account. After he pays $415 for his portion of the rent and $220 for his portion of the utilities, how much does Rufus have left in his checking account? 4. On the number line shown, p is halfway between 0 and 8. What is the value of p? 0 p 8 5. $ What is the total cost of 2 large bowls priced $14 each and 14 small jars priced $2 each?

3 6. The sum of an integer n and four is equal to the difference of ten and two. What is the value of n? 7. apples The ratio of apples to pears in Celia s basket is 3:5. If there are 20 pears, how many apples are there in Celia s basket? 8. If 462 = 7 11 p, what is the value of p? 9. What is the value of ? 10. The arithmetic mean of 9, 11, 13, x and 7 is 10. What is the value of x?

4 11. If p and q are real numbers and 3( p + 4) + 4( p + 11) = 7( p + q), what is the value of q? 12. in 3 A box of Yummy Number Crunch is a rectangular prism with height 10 inches, width 8 inches and depth 3 inches. What is the volume of the box? 13. If z 16 = 4, what is the positive integer value of z? z 14. cents Meredith buys a bag containing eight apples for $3.50. When she gets home, she realizes one of the apples is rotten, so she throws it away. What is the actual cost for each non-rotten apple, in cents? 15. By switching two of the digits of the number 123,456, Rodrigo obtains a new number that is 1980 more than the original. What is the product of the two digits Rodrigo switched?

5 16. degrees In triangle ABC, m A = 35 degrees and m B = 95 degrees. What is the measure of C? 17. amounts Dak has a quarter, a dime, a nickel and a penny. How many different amounts can be obtained by using one or more of the coins in Dak s collection? 18. The sum of two numbers is 14, and their difference is 4. What is their product? 19. What is the value of ? 20. The arithmetic mean of a and b is 6.2, the mean of b and c is 7.3 and the mean of a and c is 4.5. What is the value of a + b + c?

6 21. What is the greatest integer value of x for which 3 x < 100? 22. Which digit should replace A in the units place of the number 987,654,32A so that the number is divisible by 6? 23. rectangles How many rectangles of any size are in the figure shown? 24. In the equation shown, if p and q are positive integers and p is odd, what is the value of the sum p + q? = p 2 q 25. $ Three employees split a bonus valued at some number of dollars. Arman first receives $10 more than one third of the total amount. Bernardo then receives $3 more than one half of what was left. Carson receives the remaining $25. What is the total dollar value of the bonus?

7 26. A line is tangent to a circle at the point (2, 5). A parallel line is tangent to the circle at (8, 13). What is the common slope of the two lines? Express your answer as a common fraction. 27. For a particular list of four distinct integers the mean, median and range have the same value. If the least integer in the list is 10, what is the greatest value for an integer in the list? 28. units 2 In circle P, chords AB and CD intersect at E so that AD = AE = 3, ED = 4 and BC = 5. What is the area of triangle BCE? Express your answer as a common fraction in simplest radical form. 29. There are two values of x such that x 2018 x 2019 = 1. What is the absolute 6 difference between these two values of x? Express your answer as a common fraction. 30. Six standard six-sided dice are rolled, and the sum S is calculated. What is the probability that S (42 S ) < 297? Express your answer as a common fraction.